Dog and Goat

We have an Anglo-Nubian billygoat who has grown up with our dogs, a White Shepherd and a Jack Russel X who both are friendly and sociable bitches. They always got along with the goat beautifully, and as the goat has grown very large and strong (he is about 60kg in weight now compared to 35kg and 10kg in the dogs) it seems that he has meanwhile become the "top dog" in our pack. This has happened without any fights, naturally and peacefully, over the course of time.
A few days ago, a very energetic, 3 year old, undesexed male White Shepherd Dog joined our family. My bitches submitted themselves to him without any discussion straight away, and maintained peace and friendliness from Day One, but whenever I let the goat, "Nibbles", and the new boy-dog, "Prince", out in the backyard at the same time, they will start a serious fight.
The goat will go on his back hooves, stand up 2 metres high and try to jump on Prince, or he will headbutt Prince with his head and his (amputated and curved backwards, therefore not sharp) horn, or kick him with his hooves.
At the same time, Prince will jump on the goat's neck and try to kill him, or he will bite him in his legs. In this state of aggression, he is unapproachable and will not listen to any command from my side.
As both these animals are large and strong, it is very hard for me to get them apart. I actually got injured myself when I first tried, and again, when it happened the second time. I had to hit them with sticks and garden tools and kick them to save their lives. It was not a pleasant situation for neither of us. Therefore, since then, I keep them cautiously apart. There is no problem at all as long as there is a fence between them; the dog won't even bark at the goat. However, they will have to share the limited space of our backyard, and life would be much more pleasant for both of them if I would not have to lock away at least one of them at any time. I wished Prince and Nibbles would become friends and would learn to play together nicely, and sleep calmly side-by-side, just as Nibbles uses to do with my other dogs.
Does anyone have any advice for me, how I can support them to become friends, in a safe way, with no injuries and bad feelings on either side?

Nibbles is naturally fearful of a strange large predator. I have miniature donkeys and sheep, dogs are not welcome in the pasture. The donkeys have attacked dogs in the pasture, rams will attack dogs, and mother ewes will attack.
These animals will learn to tolerate family dogs, and in your case become buddies. But, you introduced a grown(?) assertive dog who has not been socialized to goats to an animal that is typically on the menu in normal circumstances. Nibbles has learned that this new predator will -yes- try to kill him. You need to teach Prince that he is not allowed in the pen. Period. A sound minded GSD should learn quickly that he is not allowed in that pen.

Yes, I understand, thank you. The problem is only that it will be difficult for us to keep both of them if they can't become friends, because we don't have very much space. The dog came back to us unplanned; we bred him and sold him as a puppy 3 years ago, and last week an RSPCA shelter in NSW called us that he was surrendered there because of family breakup etc, so I drove 1,600km to pick him up. We have only a backyard of about 500 sqm, which includes a fully fenced run of about 50 sqm with a solid shelter, which is now the goat's home, but which was intended for our 6 puppies who are still indoors but they are starting to get very messy now, at 4 weeks of age. I'm a bit desperate where to accommodate everyone sensibly ... It is getting very crowded here. The only other option would be to put the new big dog (41kg) on a chain (at least temporarily), then everyone else could be where they were intended to be.

I understand your predicament but I think it would be very difficult for the two of them to become buddies. The only interactions they have had were very bad. If they were both dogs I think this would be doable but I really cannot see the goat giving the new dog another chance. I know this is harsh, but the new dog is dominant (at least according to your two other dogs), young, and full of vinegar. I doubt he can be trusted any where near the goat. He needs a lot of work on the recall as well as down. He needs to down when you tell him, no matter where he is, and he especially needs the training anywhere within eyesight of the yard. Myself, I would rehome the new dog. He is still young, is healthy, and I'm sure you will train him if he is not already.
I would also set up a situation where the puppies are adjacent to the pen so they and the goat can socialize. This will give you puppies that are socialized to goats and it may make them very attractive to anyone who has goats. Okay, not many people have goats, but it is still good socializing for them.

I'm curious about this question because our neighbors a few houses down recently got a baby goat. For me this is odd because we live in the city. Do you live in the city or country? Are goats becoming the next big pet like potbellied pigs once were?

Wild, thank you for your advice, I think you are right. I now can let the goat out of the pen, while the new dog is on a chain. After a day or two of walking the goat around on a lead within good distance from the dog, the goat understood that the dog can't move away from that spot, so, the goat now grazes peacefully in the yard. At night, I lock the goat into the pen and let the dog run. I also walk him every day on a lead, and we practice obedience commands. He is a fast learner. The puppies are still indoors (in one bedroom closed off with a toddler door barrier) and go for some playtime outdoors every day. They get along well with all our other animals.
MissTonya, I would not recommend a goat as a pet for a city household. The reasons are that you can't really housebreak them and therefore will not want to keep them indoors, and being herd animals, they may become very noisy, crying for company, when left alone outdoors. And believe me, hours of constant gaot bleaking is much worse than dog barking. Further, goats can be very destructive, pull down clothes from the clothes line and eat them, kill all woodplants, and jump fences. We live in a little country town, but within the residential area, with next-door neighbours on three sides. We only could stop our goat from bleaking by giving him some doggy company, which worked well for us and our neighbours. Only since the goat has grown into an adult he has become quiet and more relaxed. Otherwise, goats are very much like dogs in their behaviour, perhaps just a bit less energetic and more stubborn, harder to train, but very affectionate and loving animals.